In this paper we address the problem of segmenting a trajectory such that each segment is in some sense homogeneous. We formally define different spatio-temporal criteria under which a trajectory can be homogeneous, including location, heading, speed, velocity, curvature, sinuosity, and\ud
curviness. We present a framework that allows us to segment any trajectory into a minimum number of segments under any of these criteria, or any combination of these criteria.\ud
In this framework, the segmentation problem can generally be solved in O(n log n) time, where n is the number of edges of the trajectory to be segmented.Postprint (published version
A good drawing of a simple graph is a drawing on the sphere or, equivalently, in the plane in which vertices are drawn as distinct points, edges are drawn as Jordan arcs connecting their end vertices, and any pair of edges intersects at most once. In any good drawing, the edges of three pairwise connected vertices form a Jordan curve which we call a triangle. We say that a triangle is empty if one of the two connected components it induces does not contain any of the remaining vertices of the drawing of the graph. We show that the number of empty triangles in any good drawing of the complete graph Kn with n vertices is at least n. 1 Jordan arcs are non-self-intersecting continuous curves containing their end points. 2 Jordan curves are continuous non-self-intersecting curves that are closed in the sense that the two "end points" are identical.
We study five existing map construction algorithms, designed and tested with urban vehicle data in mind, and apply them to hiking trajectories with different terrain characteristics. Our main goal is to better understand the existing strategies and their limitations, in order to shed new light into the current challenges for map construction algorithms.We carefully analyze the results obtained by each algorithm focusing on the local details of the generated maps. Our analysis includes the characterization of 10 types of common artifacts, which occur in the results of more than one algorithm, and 7 algorithmic-specific artifacts, which are consequences of different algorithmic strategies. This allows us to extract systematic conclusions about the main challenges to fully automatize the construction of maps from trajectory data, to detect the strengths and weaknesses of the potential different strategies, and to suggest possible ways to design higher-quality map construction methods.We consider that this analysis will be of help for designing new and better methods that perform well in wider and more realistic contexts, not only for road map or hiking reconstruction, but also for other types of trajectory data.
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